Scary! [Long response ahead sorry!!]

I might have assessed the traffic and either gone through at higher speed (adrenalin-fueled) or taken a right turn. But those were probably not possible for you at that time. It very well might have been the right thing to do.

It doesn't reallly answer your question, but you could have gone (and now: you can go) to an empty parking lot to practice braking. Go at some speed (more than 10 mph?) and try braking with different strengths, and with only the rear brake, only the front brake, different combinations of the two, etc. You will get acquainted with the actual braking power of your bike. You're right: it's not that efficient.

You will discover that if you brake only or mostly with your rear wheel, you skid. Often dangerously so. Your rear brake mainly slows you down/drags your wheel on the pavement. Try squeezing it and pedalling: you can still move forward a bit even when it's engaged. The front brake is what stops the bike for real. You have to learn to use it in combination with the rear brake, throwing your weight towards the BACK of the bike as you do it (even better with hands in the drops). Obviously you did something right because you didn't go flying over the bars. Good reflex!

It won't solve every situation. On the flats as much as possible if I need to stop somewhat quickly I use mostly the front brake. (Throwing the weight to the back prevents you from going endo.) Going downhill at high speed, you might not have a choice but to use both brakes strongly to even just slow down quickly. I had to brake in an emergency in a paceline recently in very ugly conditions: going off a bridge on a 3 feet shoulder with about 8 cyclists ahead of me and 3 behind, and traffic going 30 mph to our left. The rider in the front made a decision that was really unexpected and the riders in between did what they could but were not very experienced, did not pass the message very well, and, well, we at the back paid the price. Thankfully no one was hurt. I was probably going down at more than 20mph and I had to squeeze the brakes, my rear wheel skid quite a bit (1-2 feet to the left; if it had gone to the right I would have crashed I'm afraid). I still am not sure what I could have done better, I'm just happy I could reestablish balance, but it was sure a great demonstration of the dangers of the rear brake.